A gigantic "egg" explodes as component of a fireworks display. Theeggis in ~ rest before the explosion, and after the explosion, itbreaksinto 2 pieces, with the masses shown in thediagram,traveling in the opposite directions.

You are watching: What is the magnitude of the momentum |p⃗ a,i| of piece a before the explosion?


*

What is the momentum
*
ofpiece A before the explosion?
During the explosion, is the pressure of pieceAon item B better than, less than, or same to the pressure ofpieceB on piece A?
The inert of piece B is measured come be500
*
after the explosion. Find the momentum
*
ofpiece A after the explosion.

The ideas used to settle this problem are momentum, force and also law of preservation of momentum.

Determine the inert of piece A prior to the explosion. Compose the expression for the inert in terms of mass and velocity of item A. Use law of conservation of momentum to show that the momentum is very same for both pieces after the explosion. Hence, show that the forces are also the same. Use legislation of conservation of momentum and express the inert of A in regards to B after the explosion. Substitute the value of momentum of B after ~ the to explode to find the inert of A.


Fundamentals

Momentum is mathematically defines as,

*

Here, m is the mass of the body and also v is that velocity.

Law of preservation of momentum claims that “total momentum prior to collision is same to the complete momentum after collision”.

From the law of conservation of momentum,

*

Here,

*
and also
*
are the inert of the item A and also B before explosion and
*
,
*
space the momentum of the piece A and also B ~ explosion

The expression for the force acting on the egg is offered by,

*

Here, dP is the readjust in momentum and dt is the change in time.


(A)

The expression for momentum of item A before explosion is,

*

Here,

*
is the mass of the piece A and also
*
is the velocity the the item A prior to explosion.

The egg is at rest. So, the velocity of item A prior to explosion is zero.

Substitute 0 for

*
in
*
.

*

(B)

During the explosion, the pieces relocate in the contrary directions. This means, the momentum of the pieces space opposite in direction. The momenta of the piece are additionally equal in magnitude.

Therefore, the pressure of item A on piece B is equal and also opposite to the of item B on piece A.

(C)

From the regulation of preservation of momentum,

*

Since, the egg is at rest prior to explosion, the inert of pieces A and also B space zero before the explosion.

Substitute 0 for

*
,

*

Substitute

*
for
*
,

The inert of piece A after explosion is,

*

Ans: part A

Momentum of piece A prior to explosion is zero.

Part B

The pressure of piece A on item B is equal and also opposite to the of item B on piece A.

Part C

The momentum of item A ~ explosion is

*
.


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